I made an important omission which I must supply, and recapitulate the main facts. About 3.30 p. m. I had in camp six squadrons of the Fifth and Sixth Cavalry (about 24(P men), First Cavalry, and the Lancers. An officer coming at full speed made me such a report that I received the impres- sion that from 3,000 to 5,000 of the enemy were at hand. In about fifteen minutes the Fifth and Sixth Cavalry were sent to the front. The country there consists of swampy woods, narrow roads, and fences where there are openings. Then, as I was taking forward the First Cavalry, a sergeant of the Sixth Cavalry, who had been with Captain Gregg, reported to General Emory that the enemy were on a near road to the left, and a man of the Fifth Cavalry reported to me and to Cap- tain Merritt, aide-dc-camp, that the enemy were near at hand, also to the left, driving in infantry pickets, teamsters, & c. Thus my impression was confirmed, and considerable time was spent in getting the Sixth Pennsylvania in a position in a field, and I took the First Cavalry some distance on the road to the left, and waited till some information could be got. Not long after and together came reports from Captain Royalls com- mand that it had escaped by the Cold Harbor road; from Major Will- iams that the enemy was in force between him and iLtoyalls position (this dispatch General Emory took to General Porter), and Lieutenant Byrnes, of IRoyalls command, who had seen from three to five regi- ments of infantry; and a staff officer, that a brigade of infantry and a battery were at hand to re-enforce me. I sent them forward. Rushs Lancers and half of the First Cavalry were taken from me. I passed the infantry brigad~ went to Williams position and sought informa- tion; sent on the brigade when it arrived to Old Church, where there was then a cavalry picket. The first important information I could get was from Colonel Warren, at Old Church, about midnight, that the enemy he beheved to be lying about 1~ miles in front of him. I made arrangements to attack him at daylight with my whole force. About an hour after I learned with certainty that the enemy was not there, and had been at Garlicks Landing the afternoon before. (Lieutenant Spangler, regimental quartermaster Sixth Cavalry, who was in the neighborhood with a train, states he ~~as there about 4.30 oclock.) The average estimate of the enemys force was about 1,500 cavalry, with artillery certainly. Nothing new was ascertained as to infantry, so the rest is plain. I could not overtake him with cavalry alone, of which I had under 500. If he returned, as was then snpposed, I went on at daylight to meet him with my whole force. Since an investigation has been orderedknown to all the world I have the right to demand a thorough one, and a publication of the judgment of the case or the complete exoneration by the major-general commanding the army. Very respectfully, your obedient servant, P. ST. GEG. COOKE, Brigadier- General, U. S. Army. Brig. Gen. H. B. MARCY, Chief of Staff, Army of the Potomac.